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Register a new userBose-Einstein condensation of dilute alpha clusters above four $alpha$ threshold in $^{16}$O in field theoretical superfluid cluster model
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Observed well-developed $alpha$ cluster states in $^{16}$O, located above the four $alpha$ threshold, are investigated from the viewpoint of Bose-Einstein condensation of $alpha$ clusters by using a field-theoretical superfluid cluster model in which the order parameter is defined. The experimental energy levels are reproduced well for the first time by calculation. In particular, the observed 16.7 MeV $0_7^+$ and 18.8 MeV $0_8^+$ states with low-excitation energies from the threshold are found to be understood as a manifestation of the states of the Nambu-Goldstone zero-mode operators, associated with the spontaneous symmetry breaking of the global phase, which is caused by the Bose-Einstein condensation of the vacuum 15.1 MeV $0^+_6$ state with a dilute well-developed $alpha$ cluster structure just above the threshold. This gives evidence of the existence of the Bose-Einstein condensate of $alpha$ clusters in $^{16}$O. It is found that the emergence of the energy level structure with a well-developed $alpha$ cluster structure above the threshold is robust, almost independently of the condensation rate of $alpha$ clusters under significant condensation rate. The finding of the mechanism why the level structure that is similar to $^{12}$C emerges above the four $alpha$ threshold in $^{16}$O reinforces the concept of Bose-Einstein condensation of $alpha$ clusters in addition to $^{12}$C.
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Bose-Einstein condensation of alpha clusters in light and medium-heavy nuclei is studied in the frame of the field theoretical superfluid cluster model. The order parameter of the phase transition from the Wigner phase to the Nambu-Goldstone phase is a superfluid amplitude, square of the moduli of which is the superfluid density distribution. The zero mode operators due to the spontaneous symmetry breaking of the global phase in the finite number of alpha clusters are rigorously treated. The theory is systematically applied to N alpha nuclei from12C-52Fe at various condensation rates. In 12C it is found that the energy levels of the gas-like well-developed alpha cluster states above the Hoyle state are reproduced well in agreement with experiment for realistic condensation rates of alpha clusters. The electric E2 and E0 transitions are calculated and found to be sensitive to the condensation rates. The profound raison detre of the alpha cluster gas-like states above the Hoyle state, whose structure has been interpreted geometrically in the nuclear models without the order parameter such as the cluster models or ab initio calculations, is revealed. It is found that in addition to the Bogoliubov-de Gennes vibrational mode states collective states of the zero mode operators appear systematically at low excitation energies from the N alpha threshold energy. These collective states, new-type soft modes in nuclei due to the Bose-Einstein condensation of the alpha clusters, emerge systematically in light and medium-heavy mass regions and are also located at high excitation energies from the ground state in contrast to the traditional concept of soft mode in the low excitation energy region.
We investigate the linear-chain configurations of four-$alpha$ clusters in $^{16}$O using a Skyrme cranked Hartree-Fock method and discuss the relationship between the stability of such states and angular momentum. We show the existence of a region of angular momentum (13-18 $hbar$) where the linear chain configuration is stabilized. For the first time we demonstrate that stable exotic states with a large moment of inertia ($hbar^2/2Theta$ $sim$ 0.06-0.08 MeV) can exist.
The equation of state and phase diagram of isospin-symmetric chemically equilibrated mixture of alpha particles and nucleons are studied in the mean-field approximation. The model takes into account the effects of Fermi and Bose statistics for nucleons and alphas, respectively. We use Skyrme-like parametrization of the mean-field potentials as functions of partial densities, which contain both attractive and repulsive terms. Parameters of these potentials are chosen by fitting known properties of pure nucleon- and pure alpha matter at zero temperature. The sensitivity of results to the choice of the alpha-nucleon attraction strength is investigated. The phase diagram of the alpha-nucleon mixture is studied with a special attention paid to the liquid-gas phase transitions and the Bose-Einstein condensation of alpha particles. We have found two first-order phase transitions, stable and metastable, which differ significantly by the fractions of alpha particles. It is shown that states with alpha condensate are metastable.
Recently, we have determined surface distributions of $alpha$ clusters in the ground state of $^{20}mathrm{Ne}$ from $alpha$-transfer cross sections, without investigating the properties of its excited states. In this paper we extend our comprehension of $alpha$-cluster structures in excited states of nuclei through reaction studies. In particular we focus on $^{16}mathrm{O}$, for which attention has been paid to advances of structure theory and assignment regarding $4^+$-resonance states. We study the surface manifestation of the $alpha$-cluster states in both the ground and excited states of $^{16}mathrm{O}$ from the analysis of the $alpha$-transfer reaction $^{12}mathrm{C}(^6mathrm{Li},d)^{16}mathrm{O}$. The $alpha$-transfer reaction is described by the distorted-wave Born approximation. We test two microscopic wave functions as an input of reaction calculations. Then a phenomenological potential model is introduced to clarify the correspondence between cluster-wave functions and transfer-cross sections. Surface peaks of the $alpha$-wave function of $^{16}mathrm{O}(0^+)$ are sensitively probed by transfer-cross sections at forward angles, while it remains unclear how we trace the surface behavior of $^{16}mathrm{O}(4^+)$ from the cross sections. We are able to specify that the $alpha$-cluster structure in the $0_1^+$ and $0_2^+$ states prominently manifests itself at the radii $sim 4$ and $sim 4.5$~fm, respectively. It is remarkable that the $4_1^+$ state has the $^{12}mathrm{C}+alpha$-cluster component with the surface peak at the radius $sim 4$ or outer, whereas the $^{12}mathrm{C}+alpha$-cluster component in the $4_2^+$ state is found not to be dominant. The $4_2^+$ state is difficult to be interpreted by a simple potential model assuming the $^{12}mathrm{C}+alpha$ configuration only.
The Bose-Einstein condensation of $alpha$ partciles in the multicomponent environment of dilute, warm nuclear matter is studied. We consider the cases of matter composed of light clusters with mass numbers $Aleq 4$ and matter that in addition these clusters contains $isotope[56]{Fe}$ nuclei. We apply the quasiparticle gas model which treats clusters as bound states with infinite life-time and binding energies independent of temperature and density. We show that the $alpha$ particles can form a condensate at low temperature $Tle 2$ MeV in such matter in the first case. When the $isotope[56]{Fe}$ nucleus is added to the composition the cluster abundances are strongly modified at low temperatures, with an important implication that the $alpha$ condensation at these temperatures is suppressed.
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